Special Issue: Advances in Foundations of Quantum Mechanics and Quantum Information with atoms and photons, QUANTUM 2012No Access

ON AN EXPERIMENTAL TEST OF PREQUANTUM THEORY OF CLASSICAL RANDOM FIELDS: AN ESTIMATE FROM ABOVE OF THE COEFFICIENT OF SECOND-ORDER COHERENCE

ANDREI KHRENNIKOV

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö, S-35195, Sweden

Search for more papers by this author

BÖRJE NILSSON

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö, S-35195, Sweden

Search for more papers by this author

, and

SVEN NORDEBO

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö, S-35195, Sweden

Search for more papers by this author

https://doi.org/10.1142/S0219749912410146Cited by:9 (Source: Crossref)

Abstract

We show that quantum probabilities for photon detection can be reproduced by a model in which classical random fields interact with detectors of the threshold type. This approach is applied to the old problem of distinguishing classical and quantum light sources with the aid of the coefficient of second-order coherence g⁽²⁾(0) (the problem of "existence of photon"). In our classical random field model, we obtain an estimate of this coefficient implying that it becomes strictly less than one for sufficiently small value of parameter , where is the average energy of pulses (photons) emitted by a source and is the detection threshold. This prediction can in principle be tested experimentally. Thus in the presented model experimental technicalities (such as e.g. the detection thresholds) are lifted to the level of the fundamental entities of theory.

Keywords:

References

N. Bohr , H. A. Kramers and J. C. Slater , Zeit. Phys. 24 , 69 ( 1920 ) . Google Scholar
A. Lande , Foundations of Quantum Theory ( Yale Univ. Press , 1955 ) . Google Scholar
A. Lande , New Foundations of Quantum Mechanics ( Cambridge Univ. Press. , Cambridge , 1965 ) . Google Scholar
W. E. Lamb , The Interpretation of Quantum Mechanics ( Rinton Press, Inc. , Prince- ton , 2001 ) . Google Scholar
W. E. Lamb and M. O. Scully, Polarization, Matter and Radiation. Jubilee Volume in Honour of Alfred Kasiler (Press of University de France, Paris, 1969) pp. 363–369. Google Scholar
A. Einstein, Archives des sceiences physiques et naturelles 29 (1910) pp. 525–528. Google Scholar
A. Einstein, The Collected Papers of Albert Einstein. The Swiss Years: writings, 1909–1911, ed. D. Howard (Princeton University Press, Princeton, NJ, 1993) pp. 207–208. Google Scholar
N. Mukunda , Resonance 5 , 35 ( 2000 ) . Google Scholar
A. Khrennikov , Ann. Phys. 327 , 1786 ( 2012 ) . Web of Science, Google Scholar
A. Khrennikov , B. Nilsson and S. Nordebo , J. Phys.: Conf. Ser. 361 , ( 2012 ) . Google Scholar
L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge Univ. Press , Cambridge , 1995 ) . Google Scholar
S. M. Ritov , Introduction to Statistical Radiophysics ( Nauka , Fizmatlit, Moscow , 1966 ) . Google Scholar
P. M. Morse and K. U. Ingard , Theoretical Acoustics ( Mc Graw-Hill Book Company , New York, St. Louis, San Francisco, Toronto, London, Sydney , 1968 ) . Google Scholar
M. Beck , J. Opt. Soc. Am. B 24 , 2972 ( 2007 ) . Web of Science, Google Scholar
P. Grangier, Etude expérimentale de propriétés non-classiques de la lumière: interférence à un seul photon, Université de Paris-Sud, Centre D'Orsay (1986) . Google Scholar
P. Grangier , G. Roger and A. Aspect , EPL 1 , 173 ( 1986 ) . Web of Science, Google Scholar
S. Takeuchi , R. Okamoto and K. Sasaki , Appl. Opt. 43 , 5708 ( 2004 ) . Web of Science, Google Scholar
G. Brida et al. , Opt. Exp. 19 , 1484 ( 2011 ) . Web of Science, Google Scholar
A. Ling et al. , Opt. Exp. 17 , 21302 ( 2009 ) . Web of Science, Google Scholar
A. Khrennikov , J. Phys. A: Math. Gen. 38 , 9051 ( 2005 ) . Google Scholar
A. Khrennikov , Found. Phys. Lett. 18 , 637 ( 2006 ) . Web of Science, Google Scholar
A. Khrennikov , Phys. Lett. A 357 , 171 ( 2006 ) . Web of Science, Google Scholar
A. Khrennikov , Found. Phys. Lett. 19 , 299 ( 2006 ) . Web of Science, Google Scholar
A. Khrennikov , Nuovo Cimento B 121 , 505 ( 2006 ) . Google Scholar
A. Khrennikov , EPL 88 , 40005.1 ( 2009 ) . Web of Science, Google Scholar
A. Khrennikov , EPL 90 , 40004 ( 2010 ) . Web of Science, Google Scholar
A. Khrennikov, J. Russ. Laser Res. 31(2), 191 (2010). Web of Science, Google Scholar
A. Khrennikov , M. Ohya and N. Watanabe , Int. J. Quant. Inf. 9 , 281 ( 2011 ) . Link, Web of Science, Google Scholar
A. Khrennikov , M. Ohya and N. Watanabe , J. Russian Laser Research 31 , 462 ( 2010 ) . Web of Science, Google Scholar
N. Bohr , Phys. Rev. 48 , 696 ( 1935 ) . Google Scholar
A. Khrennikov, Quantum probabilities and violation of CHSH-inequality from classical random signals and threshold type properly calibrated detectors, [quant-ph] , arXiv:1111.1907v2 . Google Scholar
W. B. Davenport and W. L. Root , An Introduction to the Theory of Random Signals and Noise ( Wiley-IEEE Press , 1987 ) . Google Scholar
M. Zakai and J. Ziv , IEEE Trans. Inf. Theory IT 15 , 167 ( 1969 ) . Web of Science, Google Scholar
A. N. Shyryaev , On Martingale Methods in Problems for Boundary Crossing by Brow- nian Motion , Ser. Contemporary Math. Problems 8 ( Stecklov Math. Institute Press , Moscow , 2007 ) . Google Scholar
G. Brida et al. , J. Phys. B: At. Mol. Opt. Phys. 35 , 4751 ( 2002 ) . Web of Science, Google Scholar
G. Brida et al. , J. Phys. B: At. Mol. Opt. Phys. 37 , 3781 ( 2004 ) . Web of Science, Google Scholar
Brida et al. , Int. J. Quantum. Inform. 5 , 265 ( 2007 ) . Link, Web of Science, Google Scholar
G. Brida et al. , Opt. Exp. 16 , 11750 ( 2008 ) . Web of Science, Google Scholar
M. Genovese et al. , J. Phys.: Conf. Ser. 67 , 01204 ( 2007 ) . Google Scholar
S. V. Polyakov, A. Migdall and S. W. Nam, Advances in Quantum Theory, AIP Conf. Proc 1327 (Melville, NY, 2010) pp. 505–519. Google Scholar
U. Sinhaet al., Foundations of Probability and Physics-5, AIP Conf. Proc 1101, eds. L. Accardiet al. (Melville, NY, 2009) pp. 200–207. Google Scholar
M. D. Eisaman et al. , Rev. Sci. Instrum. 82 , 071101 ( 2011 ) . Web of Science, Google Scholar